Showing papers on "Mixture theory published in 2000"
TL;DR: In this paper, the entropy inequality was exploited to obtain restrictions on constitutive relations at the macroscale for a 2-phase, multiple-constituent, polarizable mixture of fluids and solids.
Abstract: In Part I macroscopic field equations of mass, linear and angular momentum, energy, and the quasistatic form of Maxwell''s equations for a multiphase, multicomponent medium were derived. Here we exploit the entropy inequality to obtain restrictions on constitutive relations at the macroscale for a 2-phase, multiple-constituent, polarizable mixture of fluids and solids. Specific emphasis is placed on charged porous media in the presence of electrolytes. The governing equations for the stress tensors of each phase, flow of the fluid through a deforming medium, and diffusion of constituents through such a medium are derived. The results have applications in swelling clays (smectites), biopolymers, biological membranes, pulsed electrophoresis, chromotography, drug delivery, and other swelling systems.
60 citations
TL;DR: In this paper, the authors used the theory of mixtures to model asphalt concrete and solved hyperbolic conservation equations by an upwind finite volume scheme coupled with an operator splitting technique for a quasi-static type of loading.
57 citations
TL;DR: In this article, a non-linear theory of drying is constructed based on the concept of mixture theory and the thermodynamics of irreversible processes, which is concerned with deformations and drying-induced stresses of moistened capillary-porous medium during intensive drying.
56 citations
TL;DR: In this article, a system of macroscopic equations for two-phase immiscible displacement in porous media is presented, which are based on continuum mixture theory and incorporate the spatiotemporal variation of interfacial energies and residual saturations.
Abstract: A system of macroscopic equations for two-phase immiscible displacement in porous media is presented. The equations are based on continuum mixture theory. The pairwise character of interfacial energies is explicitly taken into account. The equations incorporate the spatiotemporal variation of interfacial energies and residual saturations. The connection between these equations and relative permeabilities is established, and found to be in qualitative agreement with experiment.
41 citations
TL;DR: In this paper, the authors compare the theory for immiscible mixtures by Drumheller and Bedford with the theory of Passman, Nunziato, and Walsh, and investigate the differences in their microinertial descriptions.
33 citations
TL;DR: In this article, the authors generalized the basic approaches used in mathematical models and general methods for solution of the equations of the mechanics of stochastic composites to the problem of finding the effective moduli of a stochastically inhomogeneous medium.
Abstract: The basic approaches used in mathematical models and general methods for solution of the equations of the mechanics of stochastic composites are generalized. They can be reduced to the stochastic equations of the theory of elasticity of a structurally inhomogeneous medium, to the equations of the theory of effective elastic moduli, to the equations of the theory of elastic mixtures, or to more general equations of the fourth order. The solution of the stochastic equations of the elastic theory for an arbitrary domain involves substantial mathematical difficulties and may be implemented only rather approximately. The construction of the equations of the theory of effective moduli is associated with the problem on the effective moduli of a stochastically inhomogeneous medium, which can be solved by the perturbation method, by the method of moments, or by the method of conditional moments. The latter method is most appropriate. It permits one to determine the effective moduli in a two-point approximation and nonlinear deformation properties. In the structure of equations, the theory of elastic mixtures is more general than the theory of effective moduli; however, since the state equations have not been strictly substantiated and the constants have not been correctly determined, theoretically or experimentally, this theory cannot be used for systematic designing composite structures. A new model of the nonuniform deformation of composites is more promising. It is constructed by performing strict mathematical transformations and averaging the output stochastic equations, all the constants being determined. In the zero approximation, the equations of the theory of effective moduli follow from this model, and, in the first approximation, fourth-order equations, which are more general than those of the theory of mixtures, follow from it
33 citations
TL;DR: The use of composite finite element models where meshes with different granularities are allowed to share the same problem domain, is introduced and improved solutions may be obtained without increasing the computational cost of the problem or requiring postprocessing of the results.
13 citations
TL;DR: In this paper, a new theory of the adaptive growth of biological materials is presented, derived from the basic laws of continuum mechanics and described as a classical mixture of solid material and fluid.
Abstract: In this paper, a new theory of the adaptive growth of biological materials is presented. The theory is derived from the basic laws of continuum mechanics. The material is described as a classical mixture of solid material and fluid. It will be shown that several well-known models of the adaptive growth are embedded in this more general theory. In addition, it is clarified on which material assumptions these models are based. Finally, a solution procedure for the new theory is developed, and several examples are given.
11 citations
TL;DR: In this article, a mixture theory model for a flowing mixture of solid particulates and a fluid is developed, and the boundary value problem is solved numerically and representative results are presented.
Abstract: Mixture theory is used to develop a model for a flowing mixture of solid particulates and a fluid. Equations describing the flow of a two-component mixture consisting of a Newtonian fluid and a granular solid are derived. These relatively general equations are then reduced to a system of coupled ordinary differential equations describing Couette flow between concentric rotating cylinders. The resulting boundary value problem is solved numerically and representative results are presented.
9 citations
TL;DR: In this paper, a two-phase mixture constitutive model is proposed, in which the behavior of the austenite is assumed to be linearly elastic while that of the martensite is elastoplastic.
Abstract: Shape memory alloys (SMAs) are composed of austenite and martensite and the volume fraction of each phase evolves during thermomechanical loading histories. The constitutive behavior of a SMA is substantially the combination of the individual behavior of each of the two phases. Based on mixture theory, a two-phase mixture constitutive model is proposed, in which the behavior of the austenite is assumed to be linearly elastic while that of the martensite is elastoplastic. The pseudoelastic behavior of a Cu-Al-Zn-Mn polycrystal subjected to proportional and complex stress or strain histories is analysed, and the main features are well replicated. The proposed model is physically distinct, simple and can easily be applied in practical engineering problems.
5 citations
TL;DR: In this article, the authors considered a multiphase mixtures of immiscible constituents and derived the pressure density function of the pore-fluid in the framework of the theory of porous media.
Abstract: Geomaterials can be understood as consisting of a porous solid skeleton, with the pores saturated by a fluid. The fluid may be water, air or, a water-air mixture. The mechanical behaviour of the whole soil body, consisting of the soil skeleton and the pore-fluid, is governed by the properties of its constituents. Since the exact structure of the pore-space is not known, a homogenization over a representative elementary volume is required in order to obtain a macroscopic approach. The description of the motion of a multiphase-mixture of immiscible constituents can be performed by the Theory of Porous Media (TPM). Based on the classical mixture theory, the TPM deals with superimposed continua. Additionally, the information of the structure is included via the concept of volume fractions [1–3].
Here, the soil skeleton material is assumed to be incompressible, whereas the pore-fluid mixture is compressible according to its composition of water and air by variable volume fractions. The pressure-density-function of the pore-fluid is derived within the framework of the TPM. Furthermore, the viscous pore-fluid allows for a linear momentum exchange (interaction force) between the constituents, which, under special assumptions, leads to the well-known Darcy law.
TL;DR: In this article, the basic mixed plane boundary value problem of equations of statics of the elastic mixture theory is considered in a simply connected domain when the displacement vector is given on one part of the boundary and the stress vector on the remaining part.
Abstract: Abstract The basic mixed plane boundary value problem of equations of statics of the elastic mixture theory is considered in a simply connected domain when the displacement vector is given on one part of the boundary and the stress vector on the remaining part. The problem is investigated using the general displacement vector and stress vector representations obtained in [Basheleishvili, Georgian Math. J. 4: 223–242, 1997]. These representations enable us to reduce the considered problem to a system of singular integral equations with discontinuous coefficients of special kind. The solvability of this system in a certain class is proved, which implies that the basic plane boundary value problem has a solution and this solution is unique.
Journal Article•
TL;DR: In this paper, a mixture formula derived on the basis of simulation of inclusions by ellipsoids is considered and compared with the results of numerical modeling of the permittivity of periodic structures obtained by the method of integral equations, and it is shown that, for the approximate description of mixtures with a high cubic content of strongly flattened inclusions, the Maxwell-Garnett formula can be used.
Abstract: The mixture formulas derived on the basis of simulation of inclusions by ellipsoids are considered. The permittivity found by the mixture formulas is compared with the results of numerical modeling of the permittivity of periodic structures obtained by the method of integral equations. It is determined how precisely these formulas describe the Maxwell-Wagner effect, the relaxation of the mixture connected with the Debye relaxation of inclusions, and the static conduction of the mixture containing a conducting medium. Different versions of the arrangement of inclusions are considered. It is shown that, for the approximate description of mixtures with a high cubic content of strongly flattened inclusions, the Maxwell-Garnett formula can be used.
TL;DR: In this paper, a gas-filled solid material is taken into consideration including finite elastic and finite elasto-plastic constitutive equations for the solid matrix combined with convenient constitutive relations for the viscous pore-fluid and the respective interaction mechanisms between the constituents.
Abstract: The low density related to the high strength of the structure and the special features of metal foams make it possible to develop special components. To design the properties of such components, for example, the finite element method offers a cheap possibility for simulations. This requires the development of a model for foamed materials. In contrast to a microscopic approach, the Theory of Porous Media (TPM) allows a macroscopic continuum mechanical description for metal foams on the the basis of a real or a virtual homogenisation over the microstructure. In particular, a gas-filled solid material is taken into consideration including finite elastic and finite elasto-plastic constitutive equations for the solid matrix combined with convenient constitutive relations for the viscous pore-fluid and the respective interaction mechanisms between the constituents.